Question

A jar contains four orange marbles numbered one to four. The jar also contains four green marbles numbered one
to four. You randomly pick a marble. It is orange or has a number less than three.
Determine if the scenario involves mutually exclusive events. Then find the probability.

Answer 1

Answer:

1/4

Step-by-step explanation:

Answer 2

Probability of (mutually exclusive events) randomly pick a orange or number less than three is  P(A or B) = ( 3/ 4).

What is mutually exclusive event?

" Two events 'A' and 'B' are said to be mutually exclusive events if and only if they are not happening at the same time. It is written as P(A or B)."

Formula used

Probability = (Number of favourable outcome) / Total outcomes

For Mutually exclusive event

P(A or B) = P(A) + P(B)

P(A∩B) = 0

According to the question,

Let O₁, O₂, O₃, O₄ be the orange balls numbered one to four.

Let G₁, G₂, G₃, G₄ be the green balls numbered one to four.

As per condition,

Randomly pick a ball which is orange or numbered less than three is mutually exclusive event.

Let A represents the event ball to be orange.

Let B  represents the event ball to be number less than three.

Number of total outcomes = 8

Favourable outcome for event A =4

Favourable outcome for event B =2

Therefore,

P(A) = 4 / 8

P(B) = 2 /8

Substitute the value in the formula of mutually exclusive event P(A or B) we get,

P(A or B) = ( 4 / 8) + ( 2 / 8)

              = ( 6 / 8)

               = ( 3 / 4)

Hence, probability of ball to be orange or number less than 3 is

P(A or B) = 3 /4.

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